The equation to represent the cost of each drink is 3(x + 2.5) + 3x = 25.50. The cost of each drink will be $3.
In the given question, it is stated that the family spent a total of $25.50 and they bought 3 Popcorn and 3 Drinks. Each popcorn costs $2.5 more than the drink. Now, suppose the cost of one drink is 'x' then we get:
Cost of 3 Drinks = 3x
Cost of 3 Popcorn = 3(x + 2.5)
The equation to represent this will be:
=> 3(x + 2.5) + 3x = 25.50
=> 3x + 7.5 + 3x = 25.50
=> 6x = 18
=> x = 3
We get x = 3, Cost of one drink will be $3
Hence, equation representing it will be 3(x + 2.5) + 3x = 25.50, and the cost of each drink will be $3
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(6.4 × 103) ÷ (3.2 × 102)
Express your answer in scientific notation.
The required solution in scientific notation is 2 × 10¹ .
Scientific notation can be used to indicate values that are either too large or too little to be conveniently written in decimal form (typically would result in a long string of digits).
In the UK, it is also known as standard form, scientific form, and standard index form.Because it can simplify numerous mathematical operations, this base ten notation is frequently used by scientists, mathematicians, and engineers.Scientific notation for non-zero numbers takes the form m × 10n, or m times ten raised to the power of n, where n is an integer and m is a non-zero real number.The given expression is (6.4 × 10³) ÷ (3.2 × 10²)
Simplifying we get :
(6.4 × 10³) ÷ (3.2 × 10²) = 20
This can be written in the scientific notation as : 2 × 10¹
Therefore the required solution is 2 × 10¹
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What is the solution to the given equation 2(y-5)=14
Answer: y=12
Step-by-step explanation:
Distribute
Add 10 to both sides
Simplify.
Answer: y = 12
Step-by-step explanation:
2 ( [tex]y\\[/tex] - 5 ) = 14
2[tex]y\\[/tex] - 2 · 5 = 14
2[tex]y\\[/tex] - 10 = 14
(2[tex]y\\[/tex] - 10) + 10 = 14 + 10
2[tex]y\\[/tex] = 24
[tex]\frac{2y}{2} = \frac{24}{2}[/tex]
If an experiment with a random outcome is repeated a large number of times, the empirical probability of an event is likely to be close to the true probability. This mathematical theorem is called what?.
Answer: The correct answer is the Law of Large Numbers
Step-by-step explanation:
Imagine flipping a coin. There is a 50% likelihood that you would get tails. However, it doesn't happen all the time. If you flipped it just a few times, you could get all tails and have 100% tails.
However, if you experimented a lot of times (a large number), you almost certainly wouldn't get all tails. You would get close to 50%. That is the main point of the law.
The more trials you do, the more likely you will get close to the theoretical value.
Find the area and perimeter of each composite figure
The perimeter and area of each of the composite figure is:
a. Area: 138.6 mm²; Perimeter = 50.27 mm.
b. Area: 120.5 cm²; Perimeter = 42.7 cm
c. Area: 521.1 mm²; Perimeter: 95.8 mm
What is the Area of a Circle, Triangle, and a Rectangle?Area of a circle = πr²
Area of a triangle = 1/2(base)(height).
Area of a rectangle = (length)(width).
What is the Perimeter of a Composite Figure?The perimeter of a composite figure = the sum of all lengths of the sides surrounding the composite figure.
a. The area of the composite figure = area of rectangle + area of two semicircles
Two semicircles = 1 circle
Area of the rectangle = (15)(5) = 75 mm²
Area of the two semicircles = πr² = π(4.5²) = 63.6 mm²
The area of the composite figure = 75 + 63.6 = 138.6 mm².
Perimeter = 5(2) + 4(3) + (perimeter of 1 circle)
Perimeter = 5(2) + 4(3) + (2πr)
Perimeter = 5(2) + 4(3) + (2π(4.5))
Perimeter = 50.27 mm.
b. Area = area of triangle + area of square + area of half circle
Area = 1/2(base)(height) + s² + 1/2(πr²)
Base = 5 cm
Height = 7 cm
s = √(7² + 5²) = 8.6 cm [Pythagorean theorem]
r = 8.6/2 = 4.3 cm
Area = 1/2(5)(7) + 8.6² + 1/2(π(4.3²))
Area = 120.5 cm²
Perimeter = 5 + 7 + 8.6 + 8.6 + (perimeter of half circle)
Perimeter = 5 + 7 + 8.6 + 8.6 + 1/2(2πr)
Perimeter = 5 + 7 + 8.6 + 8.6 + (2π(4.3))
Perimeter = 42.7 cm
c. Area = area of triangle + area of rectangle + area of half circle
Area = 1/2(base)(height) + (length)(width) + 1/2(πr²)
Base = 32 - 20 = 12 mm
Height = 14 mm
Length = 20 mm
Width = 14 mm
r = 1/2(20) = 10 mm
Area = 1/2(12)(14) + (20)(14) + 1/2(π(10²))
Area = 521.1 mm²
Perimeter = 14 + 32 + hypotenuse of the triangle + (perimeter of half circle)
Hypotenuse = √(12² + 14²) = 18.4 mm
Perimeter of half circle = 1/2(2πr) = 1/2(2π(10)) = 31.4
Perimeter of the composite figure = 14 + 32 + 18.4 + 31.4
Perimeter of the composite figure = 95.8 mm
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An architect
makes a model
of a new house
with a patio
made with
pavers. In
the model, each
paver in the
1
patio is in.
4
1
long and in.
6
wide. The actual
2
9
ft
1
The constant of proportionality is
(Type the ratio as a simplified fraction.)
3
ft
a. What is the constant of proportionality that relates the length of
a paver in the model and the actual length? Write an equation that
represents this relationship.
Answer - The constant proportionality constant of proportionality between the actual dimensions of the pavers and the model is 9. The proportionality constant for the area is 81.
Step-by-step explanation: To solve this problem, let's transform all quantities to the same units (inches)
The actual dimensions of the pavers are:
Then we divide the real dimensions between those of the model:
Width:
Long =
Then, the constant of proportionality between the actual dimensions of the pavers and the model is 9.
Actual length = model length * (9)
The "A" area of a paver is the product of its width multiplied by its length.
So:
(real width) * (real length) = ((9) Model width) * ((9) model length)
(real width) * (real length) = * (Model width) * (model length)
(real area) = 81 * (Model area)
The proportionality constant for the area is 81.
jaylin has a wooden cube which is painted blue on the outside. she cuts the cube into $1000$ identical cubes, some of which have some sides painted blue, then rolls the resulting cubes like dice. the probability that no blue faces land up after jaylin rolls the $1000$ cubes can be expressed as $2^a \times 3^b \times 5^c$ where $a$, $b$ and $c$ are integers. what is the value of $a b c$?
The probability is a + b + c = -382
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
Every cube's side is [tex]\sqrt[3]{1000}[/tex] = 10
Since there are 512 unpainted cubes within, the likelihood is 1⁵¹² = 1
There are 8 corners, and each one has a chance of 3 / 6 = 1 / 2 = 2⁻¹ so the probability is 1⁸ / 2 = 1 / 2⁸
There are 8 * 12 = 96 edge pieces (12 edges total, with 8 on each edge; each cube has a probability of 4 / 6 = 2 / 3, so the probability is 2⁹⁶ / 3 = 2⁹⁶ / 3⁹⁶
There are 8 * 8 * 6 = 384 center cubes, each having a chance of 5 / 6, so the probability is 5³⁸⁴ / 6 = 5³⁸⁴ / 6³⁸⁴ = 5³⁸⁴ / (2³⁸⁴ * 3³⁸⁴)
So, the probability is:
(1 / 2⁸) * (2⁹⁶ / 3⁹⁶) * [5³⁸⁴ / (2³⁸⁴ * 3³⁸⁴)]
= (5³⁸⁴ * 2⁹⁶) / (2³⁹² * 3⁴⁷⁰)
= 5³⁹⁴ * 2⁹⁶ * 2⁻³⁹² * 3⁻⁴⁷⁰
= 5³⁸⁴ * 2⁻²⁹⁶ * 3⁻⁴⁷⁰
Thus, a + b + c = -382
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Create a division problem where both the divisor and the dividend are decimals. the quotient must be a whole number greater than 1. step by step please!
The Divisor is 1.5 , the Dividend is 4.5 and the quotient is 3.
As per the question we need to create a division problem where both the divisor and the dividend are decimals and the quotient must be a whole number greater than 1.
So, Let us suppose divisor as 1.5 . Now the dividend must be a decimal number which is greater than 1.5, let's say 5.5.
Now on dividing 5.5 by 1.5,
Divisor = 1.5
Dividend = 4.5
(Dividend/Divisor) = ( 4.5 / 1.5 ) = 3
Quotient = 3
On dividing dividend by divisor the quotient is 3 which is a whole number greater than 1.
So, we can conclude that the Divisor is 1.5 , the Dividend is 4.5 and the quotient is 3.
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question is in the photo
The values for the parabola are found as-
Focus, a = 4x axis vertex; h = 5y-axis vertex; k = 8What is meant by the parabola?A parabola is a curve equation in which a point on a curve is equidistant out of a fixed point and a fixed line. The fixed point is known as the parabola's focus, and also the fixed line is known as the parabola's directrix. It is also worth noting that the fixed point does not lie just on fixed line.The focus of the parabola is the point (a, 0).The parabola's directrix is the line sketched parallel to a y-axis and passing through point (-a, 0). The directrix is perpendicular to a parabola's axis.For the given question.
The total horizontal distance covered by water is 10 feet.
The maximum height attained by nozzle of water is 8 feet.
Thus, the vertex of parabola (h, k) = (5, 8)
The nozzle was 4 foot above the ground, a = 4.
The equation of parabola becomes;
y = a(x - h)² + k
y = 4(x - 5)² + 8
Thus, the equation of parabola becomes; y = 4(x - 5)² + 8.
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PLEASE HELP ASAP math isn’t going so well
Answer:
b
Step-by-step explanation:
The graph was reflected over the y-axis.
HELP WITH MATH PLEASE
Answer: 5 and the power is 2
the power used is 2
Step-by-step explanation:
use the range rule of thumb to find the minimum usual value μ–2σ and the maximum usual value μ 2σ. enter answer as an interval using square-brackets only with whole numbers.
The range thumb rule The minimum and maximum values for the usual value, which is two, are 812.14 and 885.85, respectively.
Range thumb rule: what is it?An efficient way to calculate the range from the standard deviation is to use the range rule of thumb. The range is normally around four times the standard deviation, according to this information. Inferring that your range is around eight if your standard deviation is 2, for example.
As an illustration of a binomial distribution, we'll utilize seeds.
According to given data;
Let "X" represent the number of tomato seeds that actually germinate based on the data provided.
With the knowledge provided above, we can now determine the:
The median number of seeds that we may anticipate to germinate
standard deviation (σ): sqrt of n*p*(1-p)
Once you calculate the mean and standard deviation, you can calculate the minimum usual value and the max usual value.
Now, in your problem:
n = 1415
p = 3/5
so,
the mean would be: (1415)(3/5) = 849
the standard deviation would be: sqrt (mean)(1-3/5) = 18.4282
Next, we find the minimum and maximum usual values according to the equations you gave:
minimum: mean - 2(standard deviation)
= 849 - 2(18.4282)
= 812.1436
maximum: mean + 2(standard deviation)
= 849 + 2(18.4282)
= 885.8564
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The range of a set of numbers is 19.
The minimum value is 9.
What is the maximum value?
If the range of the data set is 19. Then the maximum value of the set will be 28.
What are statistics?Statistics is the study of collection, analysis, interpretation, and presentation of data or discipline to collect and summarise the data.
The range of the data is the difference between the maximum number to the minimum number. Then the formula is written as,
Range = Maximum value - Minimum value
The range of a set of numbers is 19. And the minimum value is 9.
Then the maximum value of the set is calculated as,
Range = Maximum value - Minimum value
19 = Maximum value - 9
Maximum value = 19 + 9
Maximum value 28
If the range of the data set is 19. Then the maximum value of the set will be 28.
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Anyone know the answer for this
Can someone help me pleaseeeeee
Answer:
a) 225 meters
b) -162°C
Step-by-step explanation:
a) 5 meters per second for 45 seconds. 5*45 = 225 meters
b) cooled by 18°C per hour over a 9 hour period. -18*9 = -162°C
Answer:
a) 225 meters.
B) -2 °
Step-by-step explanation:
a If it is moving 5 meters per second, then in one second it moves 5 meters, in 2 seconds it move 10 meters, in 3 seconds it move 15 minters.
So to find how much it moved in 454 seconds we would multiply 45 x 5 = 225
B) In 9 hours it cooled 18 degrees 18/9 = 2. This means that is cooled 2 degrees per hour.
Three times the middle integer of three consecutive integers equals four less than twice the sum of the smallest and largest. find the integers
Integers are 3, 4 and 5.
What are integers?Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The boldface Z is a common mathematical symbol for the set of integers. An integer is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043.
Given Data
Let the three consecutive integers are :
x, x+1 and x+2
According to question
3(x+1) = 4 - 2(x+x+2)
3x + 3 = 4 - 2(2x + 2)
3x + 3 = 4 - 4x - 4
3 = 4x-3x
x= 3
Integers are 3, 4 and 5.
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The diameter of
one species of bacteria is shown. Bonnie
approximates this measure as 3 × 10-11 meter.
Is she correct? Explain.
No, i don't think she is correct as she didn't rounded-off correctly while measuring the diameter of bacteria.
What is rounding- off?Rounding off is a type of estimation. Estimation is used in everyday life and also in subjects like Mathematics and Physics. Many physical quantities like the amount of money, distance covered, length measured, etc are estimated by rounding off the actual number to the nearest possible whole number.
According to the picture it shows the diameter of the bacteria is 0.00000025691m
So , [tex]2.5691 * 10^-^7m[/tex] is rounded off and will be equal to [tex]3*10^-^7m\\[/tex]
As, The digit right to 2 is 5 and which already passed halfway up
So, the number 2 will be rounded off to 3 as it being the nearest digit.
Therefore, Bonnie is wrong as she did mistake while rounding - off measurments.
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Select the correct answer. paula used these steps to solve an equation: step 1: step 2: step 3: step 4: step 5: between which two steps did paula use the division property of equality? a. steps 1 and 2 b. steps 2 and 3 c. steps 3 and 4 d. steps 4 and 5
In linear equations, x = 9.5 Paula use the division property of equality.
What is a formula for linear equations?
A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. (b). Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.The Division Property of Equality states that when both sides of an equation are divided by the same nonzero number, both sides remain equal.
That is, if a, b, and c are real numbers such that a = b and c ≠0, then
a/b = c/d
The equation was -6x = 57
To move to step 5, Paula had to divide both sides by the co-efficient of x (-6) in order to get the value of x. See below
-6x = 57 ( Divide both sides by -6)
-6x/6 = 57/-6
x = 9.5
Hence, we can conclude that the division property of equality.
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The complete question is -
Paula used these steps to solve an equation:
Step 1: -4(7 + 8) - 21 = 25
Step 2: -4r – 32 - 2x = 25
Step 3: -61 – 32 = 25
Step 4: -6x = 57
Step 5: x = -95
Between which two steps did Paula use the division property of equality?
marlena surveyed classmates and found that the ratio of the numbers of text messages sent by girls varies directly with the number of texts sent to boys. The girls sent 27 texts for 9 texts sent by the boys.How Many texts did the girls send if the boys sent 7 texts
solve for x
pls hurry
Answer:
12
Step-by-step explanation:
Answer:
x = 19
Step-by-step explanation:
Alternate Exterior Angles Theorem
When a transversal line intersects two parallel lines, the resulting alternate exterior angles are congruent.
Therefore:
⇒ 8x + 11 = 5x + 68
⇒ 8x + 11 - 5x = 5x + 68 - 5x
⇒ 3x + 11 = 68
⇒ 3x + 11 - 11 = 68 - 11
⇒ 3x = 57
⇒ 3x ÷ 3 = 57 ÷ 3
⇒ x = 19
How is a line segment different from a line? How is a line segment different from a ray?
Answer:
ray:
Part of a line, containing one endpoint and extending to infinity in one direction.
line segment
Two points on a line, and all the points between those two points.
Step-by-step explanation:
in a survey of u.s. cities it is discovered there is a positive correlation between the number of paved streets in the city and the number of registered cars.does this mean that paving more streets will result in the increase of registered cars?
Yes if there is a positive correlation existing between the paving of streets and the number of registered cars then paving more streets would result in the increase in the registered cars.
What does a positive correlation mean?This is the term that is used to tell us that there is the presence of a correlation that would make the two variables that we are talking about to move in the same direction. That is when one increases, the other would have to increase as well.
Such that we would have the increase in the number of paved street to cause an increase in the number of registered cars in the place.
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QR = 5x - 15, and QS = 100
The value of x if R is the midpoint of QS is 31 units.
How to find value of x using midpoint?The midpoint is the middle point of a line segment.
It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.
The midpoint is halfway between the two end points.
Therefore, R is the midpoint of QS
Hence,
QS = QR + RS
QR = 5x - 15
QS = 100
Therefore, QR and RS are congruent because R is the midpoint of QS
QR = RS
Hence,
100 = 5x - 15 + 5x - 15
100 = 10x - 30
100 + 30 = 10x
130 = 10x
divide both sides by 10
x = 130 / 10
x = 13
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I need the answer asapplease and thank you!!!
In mathematics, a line's slope, also known as its gradient, is numerical representation of line's steepness and direction. The equation will be [tex]y= \frac{-1}{3}x +5[/tex].
What is a slope?In mathematics, a line's slope, also known as its gradient, is numerical representation of line's steepness and direction. The letter m is the frequently used to represent slope; the reason for this usage is unclear, although it can be found in O'Brien's (1844) and Todhunter's (1888) formulations of the equation for the straight line as "[tex]y = mx + b[/tex]" and "[tex]y = mx + c[/tex]," respectively.
The ratio of "vertical change" to "horizontal change" between the (any) two unique points on a line is used to compute slope. The ratio can also be written as a quotient ("rise over run"), which produces the same number for every two distinct points on the same line. A declining line has a negative "rise." The line might be useful, as determined by a road surveyor, or it might appear in a diagram that represents a road or a roof as a description or design.
Let, x= -3, x1= -2, y= 5, y1= 2
Then,
slope= [tex]\frac{x-x1}{y-y1} = \frac{-3-(-2)}{5-2} =\frac{-1}{3}[/tex]
now,
y= mx+c
y= [tex]\frac{-1}{3}[/tex]x+ 5
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consider a spinner that, after a spin, will point to a number between 0 and 1 with uniform probability. 1. what is the probability that the spinner will land on something less than 0.75? 2. determine p(1/5
Hence the probability that the spinner will land on something less than 0.75 is 37/50
As we know in between 0 and 1 the decimal numbers are ( 0.1, 0.2, 0.3, 0.4 _ _ _ _ _ 0.95, 0.96, 0.97, 0.98, 0.99, 1.00)
So,
To find the probability = favorable outcomes/ total numbers of outcomes
Favorable outcomes = 0.74 / 1.00
solve the decimal numbers in the simplified form
The probability that the spinner will land on something less than the decimal number 0.75 is 37/50.
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804
X 79
Explain step by step
The correct answer to task 804 × 79 is 63,516.
Understanding the multiplication of numbersWhen we multiply a number and another together, or a number and a variable, or even a variable with another variable, we mean the product of the two factors. The multiplication sign is " × " .
The step by step explanation of the task above is given below:
804 × 79 = 63,516.
Another example of Multiplication is
40 × 2 = 80.
The product of a and b also means Multiplication.
a and b means a × b = ab.
The product or the multiplication of g and 5 means g × 5 = 5g.
In conclusion, from the detailed information and explanation given above, the product of 804 × 79 is 63,516.
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Water is leaking from the bottom of a conical cup that is 20 inches across and 20 inches deep. Given that the cup loses 0. 5 cubic inches of water per minute, at what rate is the water level changing when the water is 8 inches deep?.
If water is leaking from the bottom of a conical cup that is 20 inches across and 20 inches deep. The rate that the water level changes when the water is 8 inches deep is: 3 /32π.
Rate of change of water leveldv/dt = rate of cup loss water per minutes=0.5
r = radius when the water is 8 inches deep
Hence,
20/10 = 8/r
r = 4
Volume of conical cup
v= 1/3πr²h
dv/dt=1/3πr² dh/dt
0.5 = 1/3π × (4)² dh/dt
dh/dt =3 /32π
Therefore the rate is 3 /32π.
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Enter the values needed to find thelength CB. (Simplify your answer.)A(-3a, b)IFB(3a, b)ECB = V(4a)2 + ([?])2C(-a, -5b)Distance Formula: d = (x2 – xı)2 + (y2 - yı)2
We are asked to find the values needed for the length CB
The coordinates of points C and B are given as
C(-a, -5b)
Recall that the distance formula is given by
[tex]d=\sqrt{\left( {x_2 - x_1 } \right)^2 + \left( {y_2 - y_1 } \right)^2 }[/tex]For the given case,
[tex]\begin{gathered} (x_1,y_1)=\mleft(-a,-5b\mright) \\ (x_2,y_2)=\mleft(3a,b\mright) \end{gathered}[/tex]Let us substitute these coordinates into the above distance formula
[tex]\begin{gathered} CB=\sqrt[]{({x_2-x_1})^2+({y_2-y_1})^2} \\ CB=\sqrt[]{({3a_{}-(-a)})^2+({b_{}-(-5b)_{}})^2} \\ CB=\sqrt[]{({3a_{}+a})^2+({b_{}+5b})^2} \\ CB=\sqrt[]{({4a})^2+({6b})^2} \end{gathered}[/tex]Therefore, the required values are
[tex]CB=\sqrt[]{({4a})^2+({6b})^2}[/tex]Choose the multiplication problem that matches this model: I Dan studied for of an hour for 4 days in a row. How many hours did he study? Dan studied for 2 hours for 4 days in a row. How many hours did he study? O Dan studied for of an hour for 4 days in a row. How many hours did he study? O Dan studied for of an hour for 4 days in a row. How many hours did he study?
The number of bars of the same color could be used to show the number of hours that Dan studies hence he studied for 2/3 hours in four days.
What is multiplication?The term multiplication refers to the number of times that a number is added to itself. For instance, if I add four three times, I could shorten the expression as four multiplied by three.
If we look at the diagram, we can see that in each tile, there are always two bars of the same color out the whole three bars. The bars that are of the same color shows the number of hours that Dan studied.
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Liz had 140 pens and inna had 100 pens. after inna gave some of her pens to liz,liz had 3 times the amount of pens that inna had. how many pens did inna give
Answer:
40
Step-by-step explanation:
140 + x = 3*(100-x)
140 + x = 300 - 3x
x + 3x = 300 - 140
4x = 160.
x = 40.
Find the discriminant of
The discriminant of the quadratic equation is 11.1.
What is the discriminant?The discriminant is the expression that we could use to deduce the kind of roots that a quadratic equation would have. Note that when we say the roots of the equation, we are talking about the solutions of the quadratic equation. We shall now try to obtain the discriminant of this equation as we can see below.
The discriminant is given as;
√b^2 - 4ac
Given;
3x^2 - 10x + 2 = 0
a = 3
b = -10
c = 2
We have;
√(-10)^2 - 4(-3) (2)
√100 + 24
11.1
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